Fundamental Limitations on the Use of Open-Region Boundary Conditions and Matched Layers to Solve the Problem of Gratings in Metallic Screens
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Fundamental Limitations on the Use of Open-Region Boundary Conditions and Matched Layers to Solve the Problem of Gratings in Metallic ScreensAbstract
Interest in accurate modeling of the electromagnetic wave scattering from grating surfaces has been renewed due to recent advances in the manipulation and localization of the light in novel application of plasmonic resonance. This work briefly reviews the frequency-domain finite methods that have been used extensively to solve the grating problem. Emphasis will be placed on the finite methods that use local boundary operators or matched layers to truncate the computational boundary. It is shown that significant errors can be generated when using either of these two mesh truncation techniques even if the truncation boundaries are receded to avoid any evanescent waves emanating from the gratings. To quantify the error, the solutions obtained using the boundary condition or matched layers are compared to the solutions obtained using either mode matching or the surface integral equation method, both of which are devoid of truncation boundary related approximations and errors. Additionally, limitations on the use of the periodic boundary condition to truncate the mesh for periodic problems are also addressed.
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